With virtually all of the ballots cast Sunday tallied, euro-skeptic Hofer, the nominee of the anti-immigration Freedom Party, held 51.9 percent of vote to Van der Bellen's 48.1 percent.

A Hofer win would make him the first far-right head of state in the European Union since the continent-wide trade and political bloc was formed in 1993. It would also mark the best far-right showing in Austria since the end of World War II.

Sunday's faceoff came just weeks after Hofer and former Green Party chief Van der Bellen swept aside challenges from ruling Social Democrat coalition candidates Rudolph Hundstorfer and Andreas Khol. Both Hundstorfer and Khol were routed April 24 in first round voting, with each winning about 11 percent of the vote.

A huge influx of migrants from the Middle East, Africa and South Asia into western Europe has spawned a backlash against official EU policy that initially welcomed migrants to the relative safety and prosperity of western Europe.

Sentiment began shifting as Austria took in 90,000 asylum seekers last year, while neighboring Germany opened its borders to more than one million migrants, many of them fleeing Syria's long and deadly civil war.

EU officials have since negotiated a deal with Turkey under which migrants fleeing its shores by boat for Greece will be returned to in exchange for nearly $7 billion in European aid.